PROPER TWIN-TRIANGULAR G a -ACTIONS ON A 4 ARE TRANSLATIONS
An additive group action on an affine 3-space over a complex Dedekind domain A is said to be twin-triangular if it is generated by a locally nilpotent derivation of A[y, z 1 , z 2 ] of the form r∂ y +p 1 (y)∂ z1 +p 2 (y)∂ z2 , where r ∈ A and p 1 ,p 2 ∈ A[y]. We show that these actions are translati...
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| Veröffentlicht in: | Proceedings of the American Mathematical Society 2014-05, Vol.142 (5), p.1513-1526 |
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| container_title | Proceedings of the American Mathematical Society |
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| creator | DUBOULOZ, ADRIEN FINSTON, DAVID R. |
| description | An additive group action on an affine 3-space over a complex Dedekind domain A is said to be twin-triangular if it is generated by a locally nilpotent derivation of A[y, z
1
, z
2
] of the form r∂
y
+p
1
(y)∂
z1
+p
2
(y)∂
z2
, where r ∈ A and p
1
,p
2
∈ A[y]. We show that these actions are translations if and only if they are proper. Our approach avoids the computation of rings of invariants and focuses more on the nature of geometric quotients for such actions. |
| format | Article |
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1
, z
2
] of the form r∂
y
+p
1
(y)∂
z1
+p
2
(y)∂
z2
, where r ∈ A and p
1
,p
2
∈ A[y]. We show that these actions are translations if and only if they are proper. Our approach avoids the computation of rings of invariants and focuses more on the nature of geometric quotients for such actions.</description><identifier>ISSN: 0002-9939</identifier><identifier>EISSN: 1088-6826</identifier><language>eng</language><publisher>AMERICAN MATHEMATICAL SOCIETY</publisher><subject>Algebra ; Equivalence relation ; Geometric translations ; Mathematical rings ; Mathematical triviality ; Morphisms ; Polynomials ; Quotients ; Universal algebra ; Zariski topologies</subject><ispartof>Proceedings of the American Mathematical Society, 2014-05, Vol.142 (5), p.1513-1526</ispartof><rights>2014 American Mathematical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/23808382$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/23808382$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,58016,58020,58249,58253</link.rule.ids></links><search><creatorcontrib>DUBOULOZ, ADRIEN</creatorcontrib><creatorcontrib>FINSTON, DAVID R.</creatorcontrib><title>PROPER TWIN-TRIANGULAR G a -ACTIONS ON A 4 ARE TRANSLATIONS</title><title>Proceedings of the American Mathematical Society</title><description>An additive group action on an affine 3-space over a complex Dedekind domain A is said to be twin-triangular if it is generated by a locally nilpotent derivation of A[y, z
1
, z
2
] of the form r∂
y
+p
1
(y)∂
z1
+p
2
(y)∂
z2
, where r ∈ A and p
1
,p
2
∈ A[y]. We show that these actions are translations if and only if they are proper. Our approach avoids the computation of rings of invariants and focuses more on the nature of geometric quotients for such actions.</description><subject>Algebra</subject><subject>Equivalence relation</subject><subject>Geometric translations</subject><subject>Mathematical rings</subject><subject>Mathematical triviality</subject><subject>Morphisms</subject><subject>Polynomials</subject><subject>Quotients</subject><subject>Universal algebra</subject><subject>Zariski topologies</subject><issn>0002-9939</issn><issn>1088-6826</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpjYuA0NLCw0DWzMDJjYeA0MDAw0rW0NLbkYOAqLs4Ccg0tTcw5GRwDgvwDXIMUQsI9_XRDgjwd_dxDfRyDFD7MnbJPIVFB19E5xNPfL1jB3w8ktEPBRMExyFUhJMjRL9jHESzFw8CalphTnMoLpbkZZN1cQ5w9dLOKS_KL4guKMnMTiyrjjYwtDCyMLYyMCckDADHCMxY</recordid><startdate>20140501</startdate><enddate>20140501</enddate><creator>DUBOULOZ, ADRIEN</creator><creator>FINSTON, DAVID R.</creator><general>AMERICAN MATHEMATICAL SOCIETY</general><scope/></search><sort><creationdate>20140501</creationdate><title>PROPER TWIN-TRIANGULAR G a -ACTIONS ON A 4 ARE TRANSLATIONS</title><author>DUBOULOZ, ADRIEN ; FINSTON, DAVID R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-jstor_primary_238083823</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Algebra</topic><topic>Equivalence relation</topic><topic>Geometric translations</topic><topic>Mathematical rings</topic><topic>Mathematical triviality</topic><topic>Morphisms</topic><topic>Polynomials</topic><topic>Quotients</topic><topic>Universal algebra</topic><topic>Zariski topologies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>DUBOULOZ, ADRIEN</creatorcontrib><creatorcontrib>FINSTON, DAVID R.</creatorcontrib><jtitle>Proceedings of the American Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>DUBOULOZ, ADRIEN</au><au>FINSTON, DAVID R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>PROPER TWIN-TRIANGULAR G a -ACTIONS ON A 4 ARE TRANSLATIONS</atitle><jtitle>Proceedings of the American Mathematical Society</jtitle><date>2014-05-01</date><risdate>2014</risdate><volume>142</volume><issue>5</issue><spage>1513</spage><epage>1526</epage><pages>1513-1526</pages><issn>0002-9939</issn><eissn>1088-6826</eissn><abstract>An additive group action on an affine 3-space over a complex Dedekind domain A is said to be twin-triangular if it is generated by a locally nilpotent derivation of A[y, z
1
, z
2
] of the form r∂
y
+p
1
(y)∂
z1
+p
2
(y)∂
z2
, where r ∈ A and p
1
,p
2
∈ A[y]. We show that these actions are translations if and only if they are proper. Our approach avoids the computation of rings of invariants and focuses more on the nature of geometric quotients for such actions.</abstract><pub>AMERICAN MATHEMATICAL SOCIETY</pub></addata></record> |
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| ispartof | Proceedings of the American Mathematical Society, 2014-05, Vol.142 (5), p.1513-1526 |
| issn | 0002-9939 1088-6826 |
| language | eng |
| recordid | cdi_jstor_primary_23808382 |
| source | American Mathematical Society Publications (Freely Accessible); JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; American Mathematical Society Publications; EZB-FREE-00999 freely available EZB journals |
| subjects | Algebra Equivalence relation Geometric translations Mathematical rings Mathematical triviality Morphisms Polynomials Quotients Universal algebra Zariski topologies |
| title | PROPER TWIN-TRIANGULAR G a -ACTIONS ON A 4 ARE TRANSLATIONS |
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